What happens if you have 3 continuous variables? Does this take the shape of a cube or rectangular prism? What about 4 continuous variables? I don't think we can visualize 4 dimensions? As a size note, I am aware that I can use Level plots. But I still wanted to build from the plane example.
Also, how can we imagine adding a categorical variable? How would that effect the plane. Using the example from the image bellow, we could add the "make of the car" to the model. "Make" could be a vector contaning ("Toyota", "Subaru", "Chevrolet")
So we have MPG~Weight+Horsepower+Make.
Would "Make" be a new axis? Or would it instead be a group of points. For example Toyota could be red points, Subaru = blue points, and Chevrolet being black points?